Effective potential for a covariantly constant gauge field in curved spacetime

We discuss the influence of gravitational effects on the stabilization of the chromomagnetic vacuum. The one-loop effective potential for a covariantly constant SU(2) gauge field in ${\bf S}^2 \times {\bf R}^2$ and ${\bf T}^2 \times {\bf R}^2$ is calculated. A possibility of curvature-induced phase transitions between zero and nonzero chromomagnetic vacua is found ---what is also confirmed through the calculation of the renormalization group (RG) improved effective potential on constant-curvature spaces with small curvature. Numerical evaluation indicates that for some curvatures the imaginary part of the effective potential disappears (gravitational stabilization of the chromomagnetic vacuum occurs).